\(a\)) \(2\left(x+1\right)=4x+2\)
\(\Leftrightarrow4x+2=4x+2\)
\(\Leftrightarrow0x=0\)
Vậy phương trình đã cho có vô số nghiệm .
b) \(x^2-9x+8=0\)
\(\Leftrightarrow x^2-9x+9-1=0\)
\(\Leftrightarrow\left(x^2-9x+9\right)^2-1=0\)
\(\Leftrightarrow\left(x-3\right)^2-1=0\)
\(\Leftrightarrow\left(x-3+1\right)\left(x-3-1\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=4\end{matrix}\right.\)
Vậy phương trình có nghiệm x = 2 hoặc x = 4 .
c) \(\dfrac{x+2}{x+3}-\dfrac{1}{x}=\dfrac{-3}{x\left(x+3\right)}\) \(\left(ĐKXĐ:x\ne0;x\ne-3\right)\)
\(\Rightarrow x\left(x+2\right)-x-3+3=0\)
\(\Leftrightarrow x^2+2x-x=0\)
\(\Leftrightarrow x\left(x+2-1\right)=0\)
\(\Leftrightarrow x\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)
Vậy phương trình có nghiệm x = -1 .
Tick cho mình nha Hanako Aki
a/ \(2\left(x+1\right)=4x+2\)
\(\Leftrightarrow2x+2=4x+2\)
\(\Leftrightarrow2x-4x=2-2\)
\(\Leftrightarrow-2x=0\)
\(\Rightarrow x=0\)
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https://hoc24.vn/hoi-dap/question/205563.html
c/ \(\dfrac{x+2}{x+3}-\dfrac{1}{x}=\dfrac{-3}{x\left(x+3\right)}\)
\(\Leftrightarrow\dfrac{x+2}{x+3}-\dfrac{1}{x}-\dfrac{-3}{x\left(x+3\right)}=0\)
\(\Leftrightarrow\dfrac{x\left(x+2\right)-1\left(x+3\right)+3}{x\left(x+3\right)}=0\)
\(\Leftrightarrow\dfrac{x^2+2x-x-3+3}{x\left(x+3\right)}=0\)
\(\Leftrightarrow\dfrac{x^2+x}{x\left(x+3\right)}=0\)
\(\Leftrightarrow\dfrac{x\left(x+1\right)}{x\left(x+3\right)\ne0}=0\)
\(\Rightarrow x\left(x+1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x+1=0\Rightarrow x=-1\end{matrix}\right.\) Vậy pt có 2 ngiệm là:\(\left\{{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\)
a)
\(2\left(x+1\right)=4x+2\Leftrightarrow2\left(x+1\right)=4\left(x+1\right)\\ \Leftrightarrow2\left(x+1\right)-4\left(x+1\right)=0\\ \Leftrightarrow-2\left(x+1\right)=0\Leftrightarrow x+1=0\Leftrightarrow x=-1\)
Vậy phương trình có tập nghiệm là S={-1}
